How to decide Linear Separability in my Neural Net work?
I would highly recommend modeling things differently with regard to how letters are presented to the model. While the problem is more natural, perhaps, for a Convolutional or Recurrent Neural Network, there's no problem to try and run this on a feed forward network. However, the way you give letters as input will be very confusing for a network and will make learning very hard. I'd recommend using one hot encoding or even a binary encoding for the letters. If this is for more than playing around I'd try and add some info (encode whether the letter is in "aeiou" in a separate bit).

As for the hidden layers, try playing around a bit. Two systematic approaches are to start very simple and make the model more complicated, or start complicated and make your model simpler (or just normalize a lot). Look at the performance on the training set and on a separate validation set during training. If the model keeps on improving on the training data but starts to deteriorate on the validation data, you're probably over fitting. In this case you should either make the model simpler (fewer nodes, fewer layers) or regularize (start with l2 normalization on the weights). If the data doesn't perform well on the training data, you may wish to make the model more complex.

Once you've tried the feedforward network, really do try CNN or RNNs for this task.